Lattice vibrations in molecular crystals and neutron scattering

Hahn, H.

Book/Report

FZJ-2017-03286

Lattice vibrations in molecular crystals and neutron scattering

Hahn, H. (Corresponding author)FZJ*

1965
Kernforschungsanlage Jülich, Verlag Jülich

Jülich : Kernforschungsanlage Jülich, Verlag, Berichte der Kernforschungsanlage Jülich 309, p. 279-89 (1965)

Please use a persistent id in citations: http://hdl.handle.net/2128/14292

Report No.: Juel-0309-RW

Abstract: As an introduction, a description of the Vibrations of a lattice of quasi-rigid molecules in terms of molecular translations and rotations is given in the harmonic approximation valid for small amplitudes. The neutron incoherent one-phonon scanering cross-section is investigated for the case in which there is little or no mixture between rotational and translational vibrations. This is true either if the coupling parameters between the rotations and the translations are small or if the mass involved in rotation about the molecules centre of gravity is small compared to the total molecular mass, i. e. if the mass is concentrated in the middle of the molecule as for example, solid methane. Simple results are obtained only for the case of cubic lattice symmetry and of circular symmetry of thelibrational parts of the thermal clouds of the atoms. In this case, as with incoherent scattering from simple cubic lattices, the energy distribution of the scattered neutrons gives (after division by some known function of temperature and frequency) directly the frequency distribution function of the molecular crystal. However, the spectra of the centre of mass and rotational vibrations enter the cross-section with different scale factors. The coherent one-phonon cross -section is also given and examined as to how, from the variations in intensity along the scattering surfaces and from their shape, one can infer the character (rotational, translational, degree of mixing) of the vibrations contributing to them.

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